Analytic wave front set for solutions to Schroedinger equation

Details Analytic wave front set for solutions to Schroedinger equation Analytic wave front set for solutions to Schroedinger equation

2007-06-04

arxiv.org/abs/0706.0415v1

Mathematics

Analysis of PDEs

32 pages

Scientific paper

This paper is a continuation of a previous paper by the same authors, where an analytic smoothing effect was proved for long-range type perturbations of the Laplacian $H_0$ on $\re^n$. In this paper, we consider short-range type perturbations $H$ of the Laplacian on $\re^n$, and we characterize the analytic wave front set of the solution to the Schr\"odinger equation: $e^{-itH}f$, in terms of that of the free solution: $e^{-itH_0}f$, for $t<0$ in the forward nontrapping region. The same result holds for $t>0$ in the backward nontrapping region. This result is an analytic analogue of results by Hassel and Wunsch and Nakamura.

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